For example, beveling for glass plates usually requires successive working steps such as edging (edge cutting or grinding), bevel-cutting, bevel-grinding for grinding bevel-cut face (smoothing by grinder or the like) and the step for polishing the bevel-ground face. In automatic beveling for glass plates of various shapes, working heads and thus working wheels in each of the working steps have to be arranged so that they run along the glass plate edges and the movement of each of the working wheels should be controlled respectively. Since there are a number of operations to be controlled where all of the movements of the working wheels in each of the above steps are individually controlled, many and intricate and elaborate control units are required and the program for preparing a control tape is complicated and difficult.